This paper reviews the state-of-the-art in robust design optimization – the search for designs and solutions which are immune with respect to production tolerances, parameter drifts during operation time, model sensitivities and others. Starting with a short glimps of Taguchi’s robust design methodology, a detailed survey of approaches to robust optimization is presented. This includes a detailed discussion on how to account for design uncertainties and how to measure robustness (i.e., how to evaluate robustness). The main focus will be on the different approaches to perform robust optimization in practice including the methods of mathematical programming, deterministic nonlinear optimization, and direct search methods such as stochastic approximation and evolutionary computation. It discusses the strengths and weaknesses of the different methods, thus, providing a basis for guiding the engineer to the most appropriate techniques. It also addresses performance aspects and test scenarios for direct robust optimization techniques.